A new perspective on mathematics education coming from history: the example of integral calculus

This research deals with a possible use of history of mathematics in mathematics education. In particular, history can be a fundamental element for the introduction of the concept of integral through a problem-centred and intuitive approach. Therefore, what follows is dedicated to the teaching of mathematics in the last years of secondary schools, where infinitesimal calculus is addressed. The thesis here proposed is that the resort to Archimedes’ use of exhaustion method and to Newton’s initial lemmas expounded in his Principia Mathematica are useful means to reach a genetic comprehension of the concept of integral. Hence, two demonstrations by Archimedes and two lemmas by Newton are used to prove such thesis. A further idea here proposed is that history of mathematics can be of help for an interdisciplinary education